Macroscopic Magnetic Frustration

Abstract

Although geometrical frustration transcends scale, it has primarily been evoked in the micro- and mesoscopic realm to characterize such phases as spin ice, liquids, and glasses and to explain the behavior of such materials as multiferroics, high-temperature superconductors, colloids, and copolymers. Here we introduce a system of macroscopic ferromagnetic rotors arranged in a planar lattice capable of out-of-plane movement that exhibit the characteristic honeycomb spin ice rules studied and seen so far only in its mesoscopic manifestation. We find that a polarized initial state of this system settles into the honeycomb spin ice phase with relaxation on multiple time scales. We explain this relaxation process using a minimal classical mechanical model that includes Coulombic interactions between magnetic charges located at the ends of the magnets and viscous dissipation at the hinges. Our study shows how macroscopic frustration arises in a purely classical setting that is amenable to experiment, easy manipulation, theory, and computation, and shows phenomena that are not visible in their microscopic counterparts.

Doped colloidal artificial spin ice

“…Artificial spin ice systems constructed with nanomagnetic arrays [1][2][3][4][5][6][7][8], vortices in nanostructured superconductors [9][10][11], or soft matter systems [12][13][14][15][16][17] have attracted growing attention as outstanding model systems in which different types of ordered and degenerate ground states can be realized [1,8], as well as various types of avalanche dynamics [5,18,19], return point memory [20], and a variety of thermal effects [21][22][23][24][25][26].…”

Complex Ordered Patterns in Mechanical Instability Induced Geometrically Frustrated Triangular Cellular Structures

“…Given the difficulty of probing individual spin states in a system without disrupting their states [4], a number of artificial frustrated systems with individual discrete elements that can be directly monitored have been investigated to understand how spins accommodate the frustration of their interactions. These include artificial spin ice systems [4][5][6][7][8][9][10][11], colloid systems [2,12,13], and periodically arranged magnetic rotors [14]. Since geometrical frustration typically gives rise to disordered configurations, there has been growing interest in investigating mechanisms to generate order in frustrated systems.…”

Disorder, Edge, and Field Protocol Effects in Athermal Dynamics of Artificial Spin Ice

“…For example, Mellado and coworkers [70] have made a macroscopic artificial spin ice using magnetic rotors that can move out of plane, arranged with the rotor hinges on a kagome lattice. For example, Mellado and coworkers [70] have made a macroscopic artificial spin ice using magnetic rotors that can move out of plane, arranged with the rotor hinges on a kagome lattice.…”